Edge-bipancyclicity of bubble-sort star graphs

The interconnection network considered in this paper is the bubble-sort star graph. The $n$-dimensional bubble-sort star graph $B{S}_n$ is a bipartite and $(2n-3)$-regular graph of order $n!$. A bipartite graph $G$ is edge-bipancyclic if each edge of $G$ lies on a cycle of all even length $l$ with $4\leq l\leq |V(G)|$\mathrm{.}Inthispaper,weshowthatthe$n$-dimensionalbubble-sortstargraph$BS_n$isedge-bipancyclicfor$n\ge 3$andforeachevenlength$l$with$4\leq l\leq n!$,everyedgeof$BS_n$ lies on at least four different cycles of length $l$.